Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{2}\!\log(4)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 1ms a \({}^{2}\!\log(4)={}^{2}\!\log(2^2)=2\) 1p 1p b \({}^{4}\!\log(4)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 1ms b \({}^{4}\!\log(4)={}^{4}\!\log(4^1)=1\) 1p 1p c \(\log(100\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(100\,000)=\log(10^5)=5\) 1p 1p d \({}^{7}\!\log(\frac{1}{7})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 1ms d \({}^{7}\!\log(\frac{1}{7})={}^{7}\!\log(7^{-1})=-1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{6}}\!\log(\frac{1}{36})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 1ms a \({}^{\frac{1}{6}}\!\log(\frac{1}{36})={}^{\frac{1}{6}}\!\log(\frac{1}{6}^2)=2\) 1p 1p b \({}^{\frac{1}{10}}\!\log(100)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 1ms b \({}^{\frac{1}{10}}\!\log({}^{\frac{1}{10}}\!\log(100))={}^{\frac{1}{10}}\!\log(\frac{1}{10}^{-2})=-2\) 1p 1p c \({}^{2}\!\log(32\sqrt{2})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 1ms c \({}^{2}\!\log(32\sqrt{2})={}^{2}\!\log(2^5⋅2^{\frac{1}{2}})={}^{2}\!\log(2^{5\frac{1}{2}})=5\frac{1}{2}\) 1p 1p d \({}^{5}\!\log(5^{2{,}9})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{5}\!\log(5^{2{,}9})=2{,}9\) 1p |